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| | #REDIRECT [[Locked Candidates]] | | #REDIRECT [[Locked Candidates]] |
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| − | A [[solving technique]] that uses the [[intersection]]s between [[line]]s and [[box]]es.
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| − | Aliases include: '''Intersection Removal''', '''Line-Box Interaction'''. The terms '''Pointing''' and '''Claiming'''/'''Box-Line Reduction''' are often used to distinguish the 2 types.
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| − | This is a basic solving technique. When all [[candidate]]s for a [[digit]] in a [[house]] are located inside the intersection with another house, we can [[eliminate]] the remaining candidates from the second house outside the intersection.
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| − | == Type 1 (Pointing) ==
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| − | All the candidates for digit '''X''' in a box are confined to a single line (row or column). The surplus candidates are eliminated from the part of the line that does not intersect with this box.
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| − | .-------.-------.-------.
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| − | | * * * | * * * | X X X |
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| − | | | | - - - |
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| − | | | | - - - |
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| − | '-------'-------'-------'
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| − | Legend:
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| − | X : cell which may contain a candidate for digit X
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| − | - : cell which does not contain a candidate for digit X
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| − | * : cell from which we may eliminate the candidates for digit X
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| − | Depending on the number of available candidates in the intersection, this technique is also known as a '''Pointing Pair''' or '''Pointing Triple'''.
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| − | == Type 2 (Claiming or Box-Line Reduction) ==
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| − | All the candidates for digit '''X''' in a line are confined to a single box. The surplus candidates are eliminated from the part of the box that does not intersect with this line.
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| − | .-------.-------.-------.
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| − | | - - - | - - - | X X X |
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| − | | | | * * * |
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| − | | | | * * * |
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| − | '-------'-------'-------'
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| − | == Example ==
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| − | [[Image:PointingPair.png]]
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| − | There is a Locked Candidates Type 1 (Pointing) for the digit 4 as shown in yellow. The red candidates can be [[eliminate]]d.
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| − | == Type 3 (Interaction with extra [[house]]s in [[Sudoku Variant]]s) ==
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| − | There are interactions in the intersections of each extra constraint and a row, column or box. Some of these overlap the regular interactions.
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| − | In [[Windoku]], the unmarked extra constraints surrounding the 4 windows should also be considered.
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| − | In [[Sudoku-X]], but also in varants with disjoint constraints, techniques such as [[Common Peer Elimination]] and [[Crossover]] will provide new methods to use the interactions with extra constraints.
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| − | == Killer Sudoku ==
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| − | The [[cage]]s in [[Killer Sudoku]] can offer more modes of the locked candidates technique. We use two examples to illustrate such techniques, both taken from [http://www.sudocue.net/weeklykiller.php?id=1 Ruud's Assassin 1].
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| − | For the first example shown below, consider the 17[3] cage in column 8.
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| − | [[Image:KillerLockedCandidates1.png]]
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| − | The possible [[cage combinations]] of the 17[3] cage in column 8 are {2,7,8} or {3,6,8} or {4,5,8} or {4,6,7}. However, in column 8, all cells that has 7 as a candidate are the cells in the 17[3] cage. Therefore, we can strike off the combinations {3,6,8} and {4,5,8}, leaving the combinations {2,7,8} or {4,6,7}. This implies that we can eliminate 3 and 5 from all cells in the cage.
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| − | For the second example shown below, consider the 9[3] cage in column 2.
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| − | [[Image:KillerLockedCandidates2.png]]
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| − | The possible [[cage combinations]] of the 9[3] cage in column 2 are {1,3,5} or {2,3,4}. Since both combinations contain the digit 3, this means that one of the cells in the 9[3] cage must contain the digit 3. Hence, 3 can be eliminated from all other cells in column 2.
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| − | == See Also ==
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| − | * [[Naked Subset]]
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| − | * [[Common Peer Elimination]]
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| − | [[Category:Solving Techniques]]
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| − | [[Category:Single-Digit]]
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| − | [[Category:Killer Sudoku]]
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| − | [[Category:Sudoku Variants]]
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